RC Circuits · RC电路
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| RC circuit/ˌɑː ˈsiː ˈsɜːkɪt/ | RC电路 | RC diàn lù |
A capacitor charges fast at first, then dawdles
- Connect a capacitor through a resistor and it charges quickly at first, then slower and slower.
- It never quite reaches full charge — it just creeps closer and closer.
- A resistor + capacitor circuit is an RC circuit RC电路, and it introduces time into circuits.
- These circuits time windscreen wipers, camera flashes and the blink of an LED.
电容器起初充电很快,然后慢吞吞
- 让电容器通过一个电阻充电,它起初充得很快,然后越来越慢。
- 它永远不会完全充满——只是越来越靠近。
- 电阻 + 电容电路是 RC 电路,它把时间引入了电路。
- 这些电路给雨刮器、相机闪光灯和 LED 的闪烁计时。
Charging is exponential
- As a capacitor charges through a resistor, its charge rises toward a final value $Q = CV$.
- The rise is exponential: fast at first (big current), slowing as the capacitor fills.
- The current falls as the charge grows — when full, no more current flows.
- Discharging is the mirror image: charge falls exponentially toward zero.
充电是指数式的
- 当电容器通过电阻充电时,它的电荷向最终值 $Q = CV$ 上升。
- 上升是指数式的:起初快(电流大),随电容器充满而变慢。
- 电流随电荷增长而下降——充满时,不再有电流流动。
- 放电是它的镜像:电荷指数式地降向零。
Charge through a resistor · 通过电阻的电荷
Change R and C and watch the charging curve speed up or slow down. · 改变R和C，观察充电曲线加速或减速。
As a capacitor charges through a resistor, its charge rises: · 当电容器通过电阻充电时，其电荷上升：
Charge rises exponentially toward $Q = CV$, fast at first then slowing. · 电荷指数上升趋近$Q = CV$，起初很快然后变慢。
The time constant
- The time constant $\tau = RC$ sets how fast the circuit charges or discharges.
- After one time constant, the capacitor reaches about $63\%$ of its final charge.
- A bigger resistance or capacitance means a slower (longer) charge.
- Change $R$ or $C$ and you tune the timing — that is how RC timers work.
时间常数
- 时间常数 $\tau = RC$ 决定电路充放电有多快。
- 经过一个时间常数,电容器达到其最终电荷的约 $63\%$。
- 更大的电阻或电容意味着更慢(更长)的充电。
- 改变 $R$ 或 $C$,你就调节了时序——RC 定时器就是这样工作的。
An RC circuit has $R = 2\ \Omega$ and $C = 3\ \text{F}$. What is the time constant, in seconds? · 一个RC电路包含$R = 2\ \Omega$和$C = 3\ \text{F}$。时间常数是多少秒？
$\tau = RC = 2 \times 3 = 6\ \text{s}$.
The time constant of an RC circuit is $\tau = R \times \_\_$. · RC电路的时间常数是$\tau = R \times \_\_$。
$\tau = RC$ — resistance times capacitance. · $\tau = RC$ — 电阻乘以电容。
Increasing the resistance in an RC circuit makes the charging: · 增加RC电路中的电阻会使充电：
A bigger $R$ gives a bigger $\tau = RC$, so slower charging. · 更大的$R$产生更大的$\tau = RC$，因此充电更慢。
Why the resistor matters
- The resistor limits the current, so it controls how fast charge flows onto the plates.
- With no resistance the capacitor would charge instantly (an idealisation).
- With a large resistance, charging takes a long, gentle time.
- So $R$ and $C$ together set the circuit's natural "clock".
电阻为何重要
- 电阻限制电流,所以它控制电荷多快流到极板上。
- 没有电阻,电容器会瞬间充满(一种理想化)。
- 有大电阻,充电就是一段漫长而平缓的时间。
- 所以 $R$ 和 $C$ 一起设定了电路天然的"时钟"。
Select all · 所有 true statements about RC circuits. · 选择所有关于RC电路的正确陈述。
RC circuits charge exponentially with $\tau = RC$; bigger R or C is slower. Charging is never instant. · RC电路以$\tau = RC$指数充电；更大的R或C意味着更慢。充电从不是一瞬间完成的。
A charging capacitor never reaches its final charge in a finite time — it only approaches it exponentially. After one time constant it is at $\approx 63\%$, not $100\%$. "Fully charged" really means "close enough after several time constants".
充电中的电容器永远不会在有限时间内达到它的最终电荷——它只是指数式地逼近。经过一个时间常数它在 $\approx 63\%$,而非 $100\%$。"充满"其实是指"经过几个时间常数后足够接近"。
A charging capacitor reaches exactly 100% of its final charge after one time constant. · 充电电容器在一个时间常数后恰好达到最终电荷的100%。
After one time constant it is at about $63\%$; it only approaches $100\%$ over several $\tau$. · 经过一个时间常数后，它约为 $63\%$；它仅在几个 $100\%$ 内逐渐接近 $\tau$.
An RC circuit has $R = 2\ \Omega$ and $C = 3\ \text{F}$. What is its time constant?
- $\tau = RC = 2 \times 3 = 6\ \text{s}$.
After $6\ \text{s}$ the capacitor holds about $63\%$ of its final charge; after several $\tau$ it is essentially full.
一个 RC 电路 $R = 2\ \Omega$、$C = 3\ \text{F}$。它的时间常数是多少?
- $\tau = RC = 2 \times 3 = 6\ \text{s}$。
$6\ \text{s}$ 后电容器持有约 $63\%$ 的最终电荷;几个 $\tau$ 后它基本充满。
An RC circuit (resistor + capacitor) charges and discharges exponentially over time. The time constant $\tau = RC$ sets the speed: after one $\tau$ the charge is $\approx 63\%$ of its final value $Q = CV$. Bigger $R$ or $C$ means slower timing — the basis of electronic timers.
RC 电路(电阻 + 电容)随时间指数式充放电。时间常数 $\tau = RC$ 决定速度:一个 $\tau$ 后电荷是最终值 $Q = CV$ 的约 $63\%$。更大的 $R$ 或 $C$ 意味着更慢的时序——电子定时器的基础。